Poro-mechanical, thermal, and chemical processes can play a significant role when developing enhanced geothermal systems. These processes occur on various time scales and the significance of their interaction varies with the problem of interest. Of particular importance is the thermo-mechanical coupling during injection operations (time scale of months/years). In fact, the phenomena of the variation of injectivity with injection water temperature and reservoir seismicity can be attributed to thermal stresses. In this paper a three-dimensional integral equation formulation is presented for calculating thermally induced stresses associated with cooling of a fracture in a geothermal reservoir. The procedure is then implemented in a computer program and is used to treat the problem of injection into an infinite fracture. The thermally induced stresses are calculated using actual field data for an injection experiment. The resulting calculations are found to be consistent with those based on a semi-analytical solution as well as field observations.


Thermally-induced stresses significantly contribute to seismicity in petroleum and geothermal fields [1, 2]. The variation of injectivity with injection water temperature and reservoir seismicity in geothermal fields have been attributed to thermally-induced stresses. It has been has found that half the earthquakes in The Geysers field seem to be associated with cold water injection [2]. The mechanism by which seismicity occurs is well understood namely, shear slip on natural fractures resulting from a reduction in effective stress acting across the fracture. The magnitude of the thermal stresses associated with advective cooling has been estimated analytically [3] using an axisymmetric model of injection into a planar reservoir and a 1D heat flow in the rock mass. It has been shown that one- and two-dimensional heat flow models underestimate heat transfer to the fluid from the crack [4]. Thus, rock cooling and the associated thermal stresses should be studied using three-dimensional heat transfer and stress models. This requires coupling a 3D heat flow model to a 3D elasticity model. A reason for ignoring the three-dimensional nature of heat conduction in the reservoir is the difficulty in treating the infinite geothermal reservoir geometry by numerical discretization. However, it has been demonstrated [4] that by using 3D Green's function for heat conduction and the integral equation formulation the need for discretizing the 3D reservoir is completely eliminated. In this paper we present a 3D integral equation formulation for calculating thermally induced stresses associated with cooling of a planar fracture in an infinite reservoir. A brief presentation of the fluid flow/heat transfer model is also provided for the sake of completeness. Additional details regarding the heat transfer modeling can be found in [4].


A schematic view of heat extraction from a fracture or a fracture zone in rock is illustrated in Figure 1. With only a few exceptions such as the finite element solution by [5-7] and the boundary element model in [8], the heat conduction in the reservoir is typically modeled as one-dimensional heat flow perpendicular to the fracture surface [9-11].

This content is only available via PDF.
You can access this article if you purchase or spend a download.